We next discuss the concept of density.
According to the spectral theorem of self adjoint operators (see [1]}), from \(\Delta \)  we obtain a spectral measure \(E\)  whose input are Borel sets and outputs are projections on \(l^2(V)\) .
In the case where \(B=\lbrace \lambda \rbrace \)  where \(\lambda \)  is an eigenvalue, \(E(\lbrace \lambda \rbrace )\)  is the orthonormal projection onto the eigenspace of \(\lambda \) .
We will denote this eigenspace by \(E_{\lambda }\) .
Fixing a fundamental domain \(W\)  of \(\Gamma \) , the density or von Neumann trace of Borel subset \(B \subset sp(\Delta )\)  is
\( dk(B) := \dfrac{1}{|W|} tr(E(B)I_W)\) 
